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Regents Exam Questions: Properties of Integers
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Properties of Integers
1 If a and b are integers, which equation is always
true?
a b

1)
b a
2) a  2b  b  2a
3) a  b  b  a
4) a  b  b  a
7 Ramón said that the set of integers is not closed for
one of the basic operations (addition, subtraction,
multiplication, or division). You want to show
Ramón that his statement is correct. For the
operation for which the set of integers is not closed,
write an example using:
• a positive even integer and a zero
• a positive and a negative even integer
• two negative even integers
Be sure to explain why each of your examples
illustrates that the set of integers is not closed for
that operation.
2 Which set is closed under division?
1) {1}
2) counting numbers
3) integers
4) whole numbers
8 If a is an odd number, b an even number, and c an
odd number, which expression will always be
equivalent to an odd number?
1) a(bc)
3 The set of integers is not closed for
1) division
2) multiplication
3) addition
4) subtraction
2)
3)
4)
4 Under which operation is the set of odd integers
closed?
1) addition
2) subtraction
3) multiplication
4) division
ac(b) 0
ac(b) 1
ac(b) 2
9 If a and b are both odd integers, which expression
must always equal an odd integer?
1) a  b
2) a  b
3) a  b
a
4)
b
5 Under which operation is the set {1,0,1} closed?
1) multiplication
2) division
3) addition
4) subtraction
10 If n represents an odd number, which computation
results in an answer that is an even number?
1) 2  n  1
2) 2  n  1
3) 3  n  2
4) 3  n  1
6 Which statement is not true for the set of integers?
1) Every integer has an additive inverse.
2) Every integer has a multiplicative inverse.
3) The set of integers is closed under addition.
4) The set of integers is closed under
multiplication.
1
ID: A
Properties of Integers
Answer Section
1 ANS: 4
The other equations are true only if a = b.
REF: 010107a
2 ANS: 1
. (2)-(4) are not closed sets because
whole numbers,
REF: 010217a
3 ANS: 1
4 ANS: 3
and while 1 and 2 are counting numbers, integers and
is not a counting number, integer or whole number.
REF: 011523ia
An odd plus and odd is even. An odd minus an odd is even. An odd divided by an odd can be a fraction.
An odd times an odd is always odd.
REF: 010928a
5 ANS: 1
REF: 060828a
6 ANS: 2
7 ANS:
REF: 089335siii
The set of integers is not closed under division.
2
0
• a positive even integer and a zero: 2  0  , which is not an integer
1
2
• a positive and a negative even integer: 2  4   , which is not an integer
1
2
• two negative even integers: 2  4  , which is not an integer
REF: 080129a
8 ANS: 2
REF: 060113a
1
ID: A
9 ANS: 3
O O  O
REF: 060525a
10 ANS: 4
REF: 080113a
2